A theory of modular forms in Clifford analysis, their applications and perspectives

被引：0

作者：

Krausshar, RS ^{[1
]}

机构：

[1] State Univ Ghent, B-9000 Ghent, Belgium

来源：

ADVANCES IN ANALYSIS AND GEOMETRY: NEW DEVELOPMENTS USING CLIFFORD ALGEBRAS | 2004年

关键词：

Clifford analysis; automorphic forms; Vahlen groups; Minkowski type-spaces; function spaces; partial differential equations; order theory; argument principles on conformal manifolds;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This chapter is devoted to monogenic, harmonic and polymonogenic Clifford-valued automorphic forms that are related to discrete subgroups of Vahlen groups acting on half-spaces of real and complex Minkowski type spaces. In particular, Eisenstein and Poincare type series are constructed within this framework. We discuss their basic properties and provide a short overview about their range of applications to several areas from pure and applied mathematics, as for example, to number theory, to functional analysis and to order theory and pde's on manifolds.

引用

页码：311 / 343

页数：33

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[51] Theta functions with harmonic coefficients over number fields [J].